Economic strategy and game theory

Question 2. 1. (a) Consider the following strategic situation. Firm A decides whether to enter firm B's industry or not. Denote these choices e and n respectively. Firm B observes this decision. If firm A enters, then the two firms simultaneously decide whether to advertise. Otherwise, firm B alone decides whether to advertise. With two firms in the market, the firms earn profits of $3 million each if they both advertise and $5 million if they both do not advertise. If only one firm advertises, then it earns $6 million and the other earns $1 million. When firm B is solely in the industry, it earns $4 million if it advertises and $3.5 million if it does not advertise. Firm A earns $0 if it does not enter. (a) Represent the game in extensive form and find all subgame perfect equilibria. (b) Give the strategic form of the game and find all Nash equilibria. 2. (b) Suppose that instead of deciding whether to advertise, the firms decide how much to spend on adver: tising, With both firms in the industry, firm i earns profit of m= (10 - a la - a",, where a is firm is advertising level and a, is the other firm's advertising level. With firm B alone in the market and spending as on advertising, it obtains 10ag - a", in profit. Represent this new game in the extensive form. Note that the advertising choices are now continuous variables, so you must use ares to represent manufacturer can sell q tires at price p = 200 - choice of q in this case. . Calculate the manufacturers profit-maximizing them. Remember to add a dotted line where you wish to represent that one player does not observe the others choice. Characterize the subgame perfect equilibrium. ~